IEEE Transactions on Information Theory最新文献

{"title":"Group Testing With Correlation Under Edge-Faulty Graphs","authors":"Hesam Nikpey;Jungyeol Kim;Xingran Chen;Saswati Sarkar;Shirin Saeedi Bidokhti","doi":"10.1109/TIT.2024.3475822","DOIUrl":"https://doi.org/10.1109/TIT.2024.3475822","url":null,"abstract":"In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model and analyze group testing on n correlated nodes whose interactions are specified by a graph G. We model correlation through an edge-faulty random graph formed from G in which each edge is dropped with probability \u0000<inline-formula> <tex-math>$1-r$ </tex-math></inline-formula>\u0000, and in the newly formed graph, all nodes in the same component have the same state. We consider three classes of graphs: cycles and trees, d-regular graphs and stochastic block models or SBM, and obtain lower and upper bounds on the number of tests needed to identify the defective nodes. Roughly speaking, we use correlation among the states of the nodes to transform the problem into that of a smaller graph with independent node states. This enhancement is quantified through the ratio of the diminished node count to the overall count of nodes, n; thus, a lower ratio signifies superior performance. The lower bounds are derived by illustrating a strong dependence of the number of tests needed on the expected number of components. In this regard, we establish a new approximation for the distribution of component sizes in “d-regular trees” which may be of independent interest and leads to a lower bound on the expected number of components in d-regular graphs. The upper bounds are found by forming dense subgraphs in which nodes are more likely to be in the same state. When G is a cycle or tree, we show an improvement by a factor of \u0000<inline-formula> <tex-math>$log (1/r)$ </tex-math></inline-formula>\u0000. For grid, a graph with almost \u0000<inline-formula> <tex-math>$2n$ </tex-math></inline-formula>\u0000 edges, the improvement is by a factor of \u0000<inline-formula> <tex-math>$(1-r) log (1/r)$ </tex-math></inline-formula>\u0000, indicating drastic improvement compared to trees. When G has a larger number of edges, as in SBM, the improvement can scale in n.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8478-8494"},"PeriodicalIF":2.2,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Intrinsic Bayesian Cramér-Rao Bound With an Application to Covariance Matrix Estimation","authors":"Florent Bouchard;Alexandre Renaux;Guillaume Ginolhac;Arnaud Breloy","doi":"10.1109/TIT.2024.3480280","DOIUrl":"https://doi.org/10.1109/TIT.2024.3480280","url":null,"abstract":"This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure. Performance bounds for such error measure were previously obtained in the non-Bayesian case (when the unknown parameter is assumed to deterministic), and referred to as intrinsic Cramér-Rao bound. The presented result then appears either as: a) an extension of the intrinsic Cramér-Rao bound to the Bayesian estimation framework; b) a generalization of the Van-Trees inequality (Bayesian Cramér-Rao bound) that accounts for the aforementioned geometric structures. In a second part, we leverage this formalism to study the problem of covariance matrix estimation when the data follow a Gaussian distribution, and whose covariance matrix is drawn from an inverse Wishart distribution. Performance bounds for this problem are obtained for both the mean squared error (Euclidean metric) and the natural Riemannian distance for Hermitian positive definite matrices (affine invariant metric). Numerical simulation illustrate that assessing the error with the affine invariant metric is revealing of interesting properties of the maximum a posteriori and minimum mean square error estimator, which are not observed when using the Euclidean metric.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9261-9276"},"PeriodicalIF":2.2,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advanced Methods for MLE of Toeplitz Structured Covariance Matrices With Applications to Radar Problems","authors":"Augusto Aubry;Prabhu Babu;Antonio De Maio;Massimo Rosamilia","doi":"10.1109/TIT.2024.3474977","DOIUrl":"https://doi.org/10.1109/TIT.2024.3474977","url":null,"abstract":"This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9277-9292"},"PeriodicalIF":2.2,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10715588","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-Driven Neural Polar Decoders for Unknown Channels With and Without Memory","authors":"Ziv Aharoni;Bashar Huleihel;Henry D. Pfister;Haim H. Permuter","doi":"10.1109/TIT.2024.3476681","DOIUrl":"https://doi.org/10.1109/TIT.2024.3476681","url":null,"abstract":"In this work, a novel data-driven methodology for designing neural polar decoders for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a “black-box” and the designer has access to the channel for generating observations of its inputs and outputs, but does not have access to the explicit channel model. The proposed method leverages the structure of the successive cancellation (SC) decoder to devise a neural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replace the core elements of the original SC decoder, the check-node, the bit-node and the soft-decision. Along with the NSC, we devise additional NN that embeds the channel outputs into the input space of the SC decoder. The proposed method is supported by theoretical guarantees that include the consistency of the NSC. Additionally, the computational complexity of the NSC decoder does not increase with the channel’s memory size and is given by \u0000<inline-formula> <tex-math>$O(mdNlog N)$ </tex-math></inline-formula>\u0000, where N is the block length, and d and m represent the dimensions of the input and the hidden units of the implemented NNs, respectively. This sets its main advantage over successive cancellation trellis (SCT) decoder for finite state channels (FSCs) that has complexity of \u0000<inline-formula> <tex-math>$O(|{mathcal {S}}|^{3} Nlog N)$ </tex-math></inline-formula>\u0000, where \u0000<inline-formula> <tex-math>$|{mathcal {S}}|$ </tex-math></inline-formula>\u0000 denotes the number of channel states. We demonstrate the performance of the proposed algorithms on memoryless channels and on channels with memory. The empirical results are compared with the analytic polar decoder, given by the SC and SCT decoders. We further show that our algorithms are applicable for the case where there SC and SCT decoders are not applicable.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8495-8510"},"PeriodicalIF":2.2,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explicit Cyclic and Quasi-Cyclic Codes With Optimal, Best Known Parameters, and Large Relative Minimum Distances","authors":"Conghui Xie;Hao Chen;Chen Yuan","doi":"10.1109/TIT.2024.3476111","DOIUrl":"https://doi.org/10.1109/TIT.2024.3476111","url":null,"abstract":"In this paper, we construct many infinite families of distance-optimal codes with new parameters, some of which are BCH codes and quasi-cyclic codes. In particular, we report the first infinite family of binary distance-optimal BCH codes with the minimum distance 8. Secondly, several infinite families of binary BCH codes and quasi-cyclic codes are presented. Many codes in these families have optimal or best known parameters. Thirdly, we construct infinite families of binary cyclic \u0000<inline-formula> <tex-math>$left [{{n, geq frac {n+1}{2},d}}right]_{2}$ </tex-math></inline-formula>\u0000 codes with minimum distances \u0000<inline-formula> <tex-math>$d geq lceil frac {n-1}{prod _{i=1}^{s}p_{i}}rceil $ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$n=(2^{p_{1}}-1)(2^{p_{2}}-1) cdots (2^{p_{s}}-1)$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$p_{1}, ldots, p_{s}$ </tex-math></inline-formula>\u0000 are different primes. Our construction extends the main result of a recent paper published by Sun et al. to much more general binary cyclic codes with various lengths. We also construct an infinite family of binary quasi-cyclic codes with the rate around \u0000<inline-formula> <tex-math>$frac {1}{2}$ </tex-math></inline-formula>\u0000 and relative minimum distance lower bounded by \u0000<inline-formula> <tex-math>$Oleft ({{frac {1}{log _{2} log _{2} n}}}right)$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8688-8697"},"PeriodicalIF":2.2,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Round Robin Active Sequential Change Detection for Dependent Multi-Channel Data","authors":"Anamitra Chaudhuri;Georgios Fellouris;Ali Tajer","doi":"10.1109/TIT.2024.3475394","DOIUrl":"https://doi.org/10.1109/TIT.2024.3475394","url":null,"abstract":"This paper considers the problem of sequentially detecting a change in the joint distribution of multiple data sources under a sampling constraint. Specifically, the channels or sources generate observations that are independent over time, but not necessarily across channels. The joint distribution of an unknown subset of sources changes at an unknown time instant. Moreover, there is a hard constraint that only a fixed number of sources can be sampled at each time instant, but the sources can be selected dynamically based on the already collected data. The goal is to sequentially observe the sources according to the constraint, and stop sampling as quickly as possible after the change while controlling the false alarm rate below a user-specified level. Thus, a policy for this problem consists of a joint sampling and change-detection rule. A non-randomized policy is studied, and an upper bound is established on its worst-case conditional expected detection delay with respect to both the change point and the observations from the affected sources before the change. In certain cases, this rule achieves first-order asymptotic optimality as the false alarm rate tends to zero, simultaneously under every possible post-change distribution and among all schemes that satisfy the same sampling and false alarm constraints. These general results are subsequently applied to the problems of (i) detecting a change in the marginal distributions of (not necessarily independent) information sources, and (ii) detecting a change in the covariance structure of Gaussian information sources.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9327-9351"},"PeriodicalIF":2.2,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10707669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Galois Self-Dual 2-Quasi Constacyclic Codes Over Finite Fields","authors":"Yun Fan;Yue Leng","doi":"10.1109/TIT.2024.3475395","DOIUrl":"https://doi.org/10.1109/TIT.2024.3475395","url":null,"abstract":"Let F be a field with cardinality \u0000<inline-formula> <tex-math>$p^{ell } $ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$0neq lambda in F$ </tex-math></inline-formula>\u0000, and \u0000<inline-formula> <tex-math>$0le hlt ell $ </tex-math></inline-formula>\u0000. Extending Euclidean and Hermitian inner products, Fan and Zhang introduced Galois \u0000<inline-formula> <tex-math>$p^{h}$ </tex-math></inline-formula>\u0000-inner product (DCC, vol.84, pp.473–492). In this paper, we characterize the structure of 2-quasi \u0000<inline-formula> <tex-math>$lambda $ </tex-math></inline-formula>\u0000-constacyclic codes over F; and exhibit necessary and sufficient conditions for 2-quasi \u0000<inline-formula> <tex-math>$lambda $ </tex-math></inline-formula>\u0000-constacyclic codes being Galois \u0000<inline-formula> <tex-math>$p^{h}$ </tex-math></inline-formula>\u0000-self-dual. With the help of a technique developed in this paper, we prove that, when \u0000<inline-formula> <tex-math>$ell $ </tex-math></inline-formula>\u0000 is even, the Hermitian self-dual 2-quasi \u0000<inline-formula> <tex-math>$lambda $ </tex-math></inline-formula>\u0000-constacyclic codes are asymptotically good if and only if \u0000<inline-formula> <tex-math>$lambda ^{1+p^{ell /2}}!=1$ </tex-math></inline-formula>\u0000. And, when \u0000<inline-formula> <tex-math>$p^{ell } ,{cancel {equiv }},3~({mathrm { mod}}~4)$ </tex-math></inline-formula>\u0000, the Euclidean self-dual 2-quasi \u0000<inline-formula> <tex-math>$lambda $ </tex-math></inline-formula>\u0000-constacyclic codes are asymptotically good if and only if \u0000<inline-formula> <tex-math>$lambda ^{2}=1$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8698-8712"},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Methods for Bounding the Length of Impossible Differentials of SPN Block Ciphers","authors":"Senpeng Wang;Dengguo Feng;Tairong Shi;Bin Hu;Jie Guan;Kai Zhang;Ting Cui","doi":"10.1109/TIT.2024.3473940","DOIUrl":"https://doi.org/10.1109/TIT.2024.3473940","url":null,"abstract":"How to evaluate the security of Substitution-Permutation Network (SPN) block ciphers against impossible differential (ID) cryptanalysis is a valuable problem. In this paper, a series of methods for bounding the length of IDs of SPN block ciphers are proposed. Firstly, we propose the definitions of minimal representative set and partition table. Therefore, an improved partition-first implementation strategy for bounding the length of IDs is given. Secondly, we introduce a new definition of ladder and propose the ladder-first implementation strategy for bounding the length of IDs. In order to be able to apply ladder-first implementation strategy in practice, the methods for determining ladders and integrating a ladder into searching models are given. Thirdly, a heuristic algorithm called dynamic-ladder-partition implementation strategy is proposed. According to our experimental results, dynamic-ladder-partition implementation strategy is more suitable for SPN ciphers whose number of elements in partition tables is little. Fourthly, rotation-equivalence ID sets of ciphers are explored to reduce the number of models that need to be considered. As applications, we show that 9-round PRESENT, 5-round AES, 6-round Rijndael-160, 7-round Rijndael-192, 7-round Rijndael-224 and 7-round Rijndael-256 do not have any ID under the sole assumption that the round keys are uniformly random. What’s more, we obtain that 8-round GIFT-64, 12-round GIFT-128 and 14-round SKINNY-128 do not have any ID under the assumptions that GIFT and SKINNY are Markov ciphers and the round keys are uniformly random. Our methods fill crucial gaps on bounding the length of IDs with the differential properties of S-boxes considered. They enhance our confidence in the security and are valuable, especially for designers.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9165-9178"},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved Linear Key Recovery Attacks on PRESENT","authors":"Wenhui Wu;Muzhou Li;Meiqin Wang","doi":"10.1109/TIT.2024.3474701","DOIUrl":"https://doi.org/10.1109/TIT.2024.3474701","url":null,"abstract":"PRESENT is an ultra-lightweight block cipher designed by Bogdanov et al., and has been widely studied since its proposal. It supports 80-bit and 128-bit keys, which are referred to as PRESENT-80 and PRESENT-128, respectively. Up to now, linear cryptanalysis is the most effective method on attacking this cipher, especially when accelerated with the pruned Walsh transform. Combing pruned Walsh transform with multiple linear attacks, one can recover the right key for 28-round PRESENT-80 and −128. Later, this method is further improved with affine pruned Walsh transform by adding more zeros in the Walsh spectrum through rejecting some data. This leads to the 29-round attack on PRESENT-128 with full codebook, which is not regarded as a valid attack in the literature. In this paper, we follow the affine pruned Walsh transform accelerated linear method, and propose 29-round attacks on both PRESENT-80 and PRESENT-128 without using full codebook. Both attacks rely on a statistical model depicting distributions of the experimental correlation when some data are artificially rejected in its computation. Besides, detailed analysis of complexity reduction for each linear hull used in attacking PRESENT is also provided and supported by an automatic tool. Our 29-round attack on PRESENT-80 mainly benefits from this tool. According to our knowledge, both attacks are the best ones on PRESENT so far.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9195-9213"},"PeriodicalIF":2.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimax Signal Detection in Sparse Additive Models","authors":"Subhodh Kotekal;Chao Gao","doi":"10.1109/TIT.2024.3473770","DOIUrl":"https://doi.org/10.1109/TIT.2024.3473770","url":null,"abstract":"Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a sparse additive signal. Our result is nonasymptotic and applicable to the general case where the univariate component functions belong to a generic reproducing kernel Hilbert space. Unlike the estimation theory, the minimax separation rate reveals a nontrivial interaction between sparsity and the choice of function space. We also investigate adaptation to sparsity and establish an adaptive testing rate for a generic function space; adaptation is possible in some spaces while others impose an unavoidable cost. Finally, adaptation to both sparsity and smoothness is studied in the setting of Sobolev space, and we correct some existing claims in the literature.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8892-8928"},"PeriodicalIF":2.2,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}